Transcription of SOLUTION OF Partial Differential Equations (PDEs)
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1 SOLUTION OFPartial Differential Equations (PDEs) Mathematics is the Language of SciencePDEs are the expression of processes that occur across time & space: (x,t), (x,y), (x,y,z), or (x,y,z,t)2 Partial Differential Equations (PDE's)A PDEis an equation which includes derivatives of an unknown function with respect to 2 or moreindependentvariables3 Partial Differential Equations (PDE's)PDE's describe the behavior of many engineering phenomena: Wave propagation Fluid flow (air or liquid)Air around wings, helicopter blade, atmosphereWater in pipes or porous mediaMaterial transport and diffusion in air or waterWeather: large system of coupled PDE's for momentum, pressure, moisture, heat.
Partial Differential Equations (PDE's) Learning Objectives 1) Be able to distinguish between the 3 classes of 2nd order, linear PDE's. Know the physical problems each class represents and the physical/mathematical characteristics of each. 2) Be able to describe the differences between finite-difference and finite-element methods for solving PDEs.
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